Relativistic Length Contraction Calculator

What is length contraction?

In physics, length contraction is a concept that refers to the phenomenon of a decrease in length of an object being measured by an observant entity which is moving at any non-zero velocity relative to the object.

The concept is linked to Hendrick Lorentz and FitzGerald thus it is often referred to as the Lorentz contraction or Lorentz-FitzGeranld contraction.

The formula describing this phenomenon is provided below:

l = l₀/γ(v) = l₀*√(1 - v²/c²)

Where:

l₀ - is initial length when the object is static

l - is the length of the object measured by the observant entity in relative motion

v - is the relative velocity between the observant entity and the object in relative motion

c - is the speed of light. It is 299792458 meters per second or 2.998*10⁸ (m/s)

γ(v) is Lorentz factor which is calculated as:

γ(v) = 1/√(1 - v²/c²)

How does this length contraction calculator work?

Depending on the unknown variable to be calculated the user can choose from the drop down list provided to solve for moving length, stationary length or velocity:

■ In case you choose to compute the moving length (l) you have to provide the stationary length (l₀) in any measurement unit from feet (ft), inches (in), meters (m), centimeters (cm) or millimeters(mm) and the velocity (v) in m/s:

Please note that this is the formula applicable when the stationary length is measured in meters (m). In case l₀ is expressed in any other unit it is converted to meters by using these conversion rates:

1 ft = 0.3048 m

1 in = 0.0254 m

1 cm = 0.01 m

1 mm = 0.001 m

Also remember that this equation returns the value of the stationary length (l) in meters, thus in the results area it is converted and displayed in all the other measurement units available in the drop down list provided initially. To do so this relativistic length contraction calculator uses the following conversion rates:

1 m = 3.2808399 ft

1 m = 39.3700787

1 m = 100 cm

1 m = 1000 mm

■ If you want to solve for the stationary length (l₀) then you have to know the moving length (l) in feet, inches, meters, centimeters or millimeters and the velocity (v) in m/s: 

Please take account that the equation explained above:

- assumes that the moving length (l) is expressed in meters (m), thus whenever it is given in any other measurement unit it is converted to meters by using the conversion rates provided previously.

- While it returns the stationary length (l₀) in meters (m), thus in the results area it will be converted and displayed in the other measurement units.

■ Finally in case you choose to find the velocity (v) you have to input the moving length (l) and the stationary length (l₀), both non-zero values expressed in any measurement unit from feet, inches, meters,  centimeters or millimeters:

Please take account of the fact that the formula described above assumes both moving and stationary lengths are expressed in meters, thus the same conversion rule applies.

Where:

l = Moving Length

l₀ = Stationary Length

v = velocity

c = 2.998*10⁸ (m/s)